The heatmap of the
data
numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000
if (!largeSet)
{
hm <- heatMaps(data=dataframeScaled[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
xlab="Feature",
ylab="Sample",
srtCol=45,
srtRow=45,
cexCol=cexheat,
cexRow=cexheat
)
par(op)
}

Correlation
Matrix of the Data
The heat map of the data
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
#cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
cormat <- cor(dataframe[,varlist],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Original Correlation",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.5443412
The
decorrelation
DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#>
#> Included: 8 , Uni p: 0.03125 , Outcome-Driven Size: 0 , Base Size: 3 , Rcrit: 0.06724898
#>
#>
1 <R=0.544,thr=0.450,N= 2>, Top: 1( 1 )[ 1 : 1 Fa= 1 : 0.450 ]( 1 , 1 , 0 ),<|>Tot Used: 2 , Added: 1 , Zero Std: 0 , Max Cor: 0.437
#>
2 <R=0.437,thr=0.250,N= 6>, Top: 2( 2 )[ 1 : 2 Fa= 2 : 0.250 ]( 2 , 3 , 1 ),<|>Tot Used: 6 , Added: 3 , Zero Std: 0 , Max Cor: 0.351
#>
3 <R=0.351,thr=0.250,N= 6>, Top: 1( 1 )[ 1 : 1 Fa= 3 : 0.250 ]( 1 , 1 , 2 ),<|>Tot Used: 6 , Added: 1 , Zero Std: 0 , Max Cor: 0.240
#>
4 <R=0.240,thr=0.250,N= 6>
#>
[ 4 ], 0.199755 Decor Dimension: 6 Nused: 6 . Cor to Base: 4 , ABase: 2 , Outcome Base: 0
#>
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]
pander::pander(sum(apply(dataframe[,varlist],2,var)))
15144
pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))
11205
pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))
3.24
pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))
3.45
The decorrelation
matrix
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
UPLTM <- attr(DEdataframe,"UPLTM")
gplots::heatmap.2(1.0*(abs(UPLTM)>0),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
}

The correlation
matrix after decorrelation
if (!largeSet)
{
cormat <- cor(DEdataframe[,varlistc],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Correlation after IDeA",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
par(op)
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
0.2395279
Univariate
Analysis
Univariate
univarRAW <- uniRankVar(varlist,
paste(outcome,"~1"),
outcome,
dataframe,
rankingTest="AUC")
univarDe <- uniRankVar(varlistc,
paste(outcome,"~1"),
outcome,
DEdataframe,
rankingTest="AUC",
)
Final Table
univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")
##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)
| glucose |
141.3 |
31.94 |
110.0 |
26.14 |
0.0472 |
0.788 |
| mass |
35.1 |
7.26 |
30.3 |
7.69 |
0.0408 |
0.688 |
| age |
37.1 |
10.97 |
31.2 |
11.67 |
0.0000 |
0.687 |
topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]
pander::pander(finalTable)
| La_glucose |
114.7 |
32.1 |
87.6 |
25.57 |
0.1133 |
0.755 |
| age |
37.1 |
11.0 |
31.2 |
11.67 |
0.0000 |
0.687 |
| La_mass |
30.8 |
7.0 |
26.5 |
6.93 |
0.0212 |
0.686 |
dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")
pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))
theCharformulas <- attr(dc,"LatentCharFormulas")
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])
orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")
finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])
| glucose |
NA |
141.3 |
31.94 |
110.0 |
26.14 |
0.0472 |
0.788 |
0.788 |
NA |
| La_glucose |
+ glucose - (0.716)age |
114.7 |
32.13 |
87.6 |
25.57 |
0.1133 |
0.755 |
0.788 |
0 |
| mass |
NA |
35.1 |
7.26 |
30.3 |
7.69 |
0.0408 |
0.688 |
0.688 |
NA |
| age |
NA |
37.1 |
10.97 |
31.2 |
11.67 |
0.0000 |
0.687 |
0.687 |
2 |
| age1 |
NA |
37.1 |
10.97 |
31.2 |
11.67 |
0.0000 |
0.687 |
NA |
NA |
| La_mass |
- (0.194)triceps + mass |
30.8 |
7.00 |
26.5 |
6.93 |
0.0212 |
0.686 |
0.688 |
-1 |
Comparing IDeA vs
PCA vs EFA
PCA
featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE) #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous])
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)
#pander::pander(pc$rotation)
PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])
gplots::heatmap.2(abs(PCACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "PCA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")

EFA
EFAdataframe <- dataframeScaled
if (length(iscontinous) < 2000)
{
topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
if (topred < 2) topred <- 2
uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE) # EFA analysis
predEFA <- predict(uls,dataframeScaled[,iscontinous])
EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous])
EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
gplots::heatmap.2(abs(EFACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "EFA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
}

Effect on CAR
modeling
par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(rawmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
}

pander::pander(table(dataframe[,outcome],pr))
pander::pander(ptab$detail[c(5,3,4,6),])
| 5 |
diag.ac |
0.772 |
0.741 |
0.801 |
| 3 |
se |
0.560 |
0.498 |
0.620 |
| 4 |
sp |
0.886 |
0.855 |
0.913 |
| 6 |
diag.or |
9.880 |
6.849 |
14.251 |
par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(IDeAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
}

pander::pander(table(DEdataframe[,outcome],pr))
pander::pander(ptab$detail[c(5,3,4,6),])
| 5 |
diag.ac |
0.768 |
0.737 |
0.798 |
| 3 |
se |
0.507 |
0.446 |
0.569 |
| 4 |
sp |
0.908 |
0.879 |
0.932 |
| 6 |
diag.or |
10.169 |
6.909 |
14.965 |
par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(PCAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))
pander::pander(ptab$detail[c(5,3,4,6),])
| 5 |
diag.ac |
0.771 |
0.739 |
0.800 |
| 3 |
se |
0.437 |
0.376 |
0.498 |
| 4 |
sp |
0.950 |
0.927 |
0.967 |
| 6 |
diag.or |
14.722 |
9.210 |
23.533 |
par(op)
EFA
EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(EFAmodel,EFAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(EFAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
}

pander::pander(table(EFAdataframe[,outcome],pr))
pander::pander(ptab$detail[c(5,3,4,6),])
| 5 |
diag.ac |
0.750 |
0.718 |
0.780 |
| 3 |
se |
0.373 |
0.315 |
0.434 |
| 4 |
sp |
0.952 |
0.929 |
0.969 |
| 6 |
diag.or |
11.806 |
7.313 |
19.059 |
par(op)